Summary: MIDTERM EXAMINATION I, MATH 5651 (FALL 2011)
ANSWER KEY
Problem 1 (15 points)
There are 12 balls in a bowl of which 5 are red and 7 are green.
(i) Sampling 6 balls WITHOUT replacement, what is the probability of getting
2 red balls in the sample?
(ii) Sampling 6 balls WITH replacement, what is the probability of getting 2 red
balls in the sample?
Just write down the exact answers--in this particular case you do not have to
explain.
Solution
(i)
5
2
7
4
12
6
=
(combinations of 5 red balls taken 2 at a time)